In the states Best Buy is stocking the new 1070 and 1080 now, I got mine yesterday.
Using the 1070 with a AMD 8320, here is my 3d Mark score:
My initial impressions, the 1070 is probably more powerful than my CPU, lol, but its not making anything I have thrown at it unplayable, the reports of bottlenecking or choking is a little to dramatic. Getting a smooth 60+ fps on Doom with no slowdown and getting insane fps on just about any game made before June 26 2016.
If you play at 1080p.
Going to 4k, I highly doubt the CPU will perform at any acceptable levels and a upgrade would definitely be needed.
TLDR, 1070 great with any processor for 1080p, anything above you need a better cpu.